Crystals 2015, 5, 226-243; doi:10.3390/cryst5020226 OPEN ACCESS
crystals ISSN 2073-4352 www.mdpi.com/journal/crystals Article
Novel S = 1/2 Kagome Lattice Materials: Cs2TiCu3F12 and Rb2TiCu3F12 Lewis J. Downie 1, Elena I. Ardashnikova 2, Chiu C. Tang 3, Alexandre N. Vasiliev 4,5,6, Peter S. Berdonosov 2, Valery A. Dolgikh 2, Mark A. de Vries 7 and Philip Lightfoot 1,* 1
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School of Chemistry and EaStChem, University of St Andrews, St Andrews KY16 9ST, UK; E-Mail:
[email protected] Department of Chemistry, M. V. Lomonosov Moscow State University, 119991 GSP-1 Moscow, Russia; E-Mails:
[email protected] (E.I.A.);
[email protected] (P.S.B.);
[email protected] (V.A.D.) Diamond Light Source Ltd., Harwell Science and Innovation Campus, Didcot OX11 0DE, UK; E-Mail:
[email protected] Department of Low Temperature Physics and Superconductivity, Physics Faculty, M. V. Lomonosov Moscow State University, 119991 GSP-1 Moscow, Russia; E-Mail:
[email protected] Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Ekaterinburg, Russia National University of Science and Technology “MISiS”, 119049 Moscow, Russia School of Chemistry and EaStChem, University of Edinburgh, Edinburgh EH9 3JZ, UK; E-Mail:
[email protected]
* Author to whom correspondence should be addressed; E-Mail:
[email protected]; Tel.: +44-1334-463-841. Academic Editor: Helmut Cölfen Received: 18 March 2015 / Accepted: 21 April 2015 / Published: 5 May 2015
Abstract: Two new members of the A2B′Cu3F12 family of kagome-related materials have been prepared, in order to further understand the crystal-chemical relationships, phase transitions and magnetic behaviour within this family of potentially frustrated S = ½ two-dimensional quantum magnets. Cs2TiCu3F12 adopts a crystal structure with the ideal kagome lattice topology (space group R3̅m) at ambient temperature. Diffraction studies reveal different symmetry-lowering structural phase transitions in single crystal and polycrystalline forms at sub-ambient temperatures, with the single crystal form retaining rhombohedral symmetry
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and the powder form being monoclinic. In both cases, long-range antiferromagnetic order occurs in the region 16–20 K. Rb2TiCu3F12 adopts a distorted triclinic structure even at ambient temperatures. Keywords: kagome lattice; magnetic; fluoride; phase transition
1. Introduction Magnetic materials adopting crystal structures based on the kagome lattice are of interest as model systems for the study of geometric magnetic frustration [1,2]. Particular interest has been focused on kagome lattice compounds containing S = ½ ions [3–6]—for example, Cu2+ and V4+—since quantum fluctuations can often compete with the tendency towards long-range magnetic order, leading to unusual magnetic ground states such as quantum spin-liquids (QSLs) or valence-bond solids (VBS). A family of mixed metal fluorides of general composition A2B′B3F12 (B = Cu2+, B′ = a tetravalent cation) [7] has recently received attention due to the observation of an exotic VBS ground state in Rb2SnCu3F12 [8]. The first members of this family to be reported were Cs2ZrCu3F12 and Cs2HfCu3F12, which were found to be structurally analogous to the aristotype Cs2NaAl3F12 at room temperature [9]. This structure type may be considered as a derivative of the pyrochlore structure, with 1:3 ordering of cations on the B-site leading to a layered structure with kagome layers of composition [B3F12] isolated from each other by the tetravalent cations. The aristotype structure has rhombohedral symmetry, space group R3̅m, and exhibits a structurally “perfect” kagome lattice of co-planar, corner-shared equilateral triangles (Figure 1).
(a)
(b)
Figure 1. View along the ab-plane (a) and down the c-axis (b) of the aristotype structure of Cs2NaAl3F12. The range of substitutions possible at the A and B′ sites of A2B′Cu3F12 have so far been limited to A = Rb+ or Cs+ and B′ = Zr4+, Hf4+, Sn4+ and Ce4+. Earlier crystallographic studies [10] have shown that,
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although Cs2ZrCu3F12 adopts the aristotype structure at room temperature, a first-order structural phase transition occurs in cooling (~225 K), which may trigger the observed onset of a canted antiferromagnetic state at low temperatures (~24 K) rather than a QSL or other unconventional magnetic ground state. Magnetic studies have also shown long-range order rather than quantum-delocalised states for other members of the family, Cs2HfCu3F12 and Cs2SnCu3F12 [11]. In the case of Cs2ZrCu3F12, the structural phase transition, which breaks the perfection of the S = ½ kagome lattice and leads to a monoclinic unit cell, is related to the increase in Zr4+ coordination from six to seven. Cs2SnCu3F12 is also found to adopt the aristotype structure at room temperature but again the magnetic data suggest some form of structural transition below ambient temperature (~185 K). The nature of this transition was originally suggested, from single crystal X-ray diffraction (SCXD), to be a doubling of the unit cell a and b parameters [11] (hexagonal setting of the rhombohedral cell) leading to a unit cell similar to that found for Rb2SnCu3F12 (see below). However, a recent powder diffraction study has shown that although there is indeed a distortion of the kagome lattice, the adoption of a monoclinic unit cell occurs. This distortion is different from that found for Cs2ZrCu3F12 and is unrelated to an increase in coordination number at the B′ site; Sn4+ retains octahedral coordination, but an optimisation of bonding at the Sn4+ site is suggested to be the driver [12]. It should be noted that differences have been reported for structural transitions in powder and single crystal samples of Rb2SnCu3F12 [13] and so it is difficult to state whether the inconsistencies between the single crystal and powder studies on Cs2SnCu3F12 are genuine; indeed, as will be seen, this is one of the interesting aspects of this family. Rb2SnCu3F12 has been previously found [14] to display an imperfect kagome lattice at room temperature. In this case, the unit cell is rhombohedral, space group R3̅, but doubled in the ab-plane when compared to that reported for Cs2NaAl3F12. This distortion leads to four different Cu2+–Cu2+ distances being present and thus a loss in the perfectly frustrated triangular environment. The reasons behind this slightly different structure are most likely related to the smaller size of Rb+ as compared to Cs+. There is also a disorder relating to the positions some of the F− ions, which is found to be independent of temperature [13] Magnetically, Rb2SnCu3F12 has generated the most interest as it shows a very unusual VBS ground state reminiscent of a “pinwheel” [8]. Structurally, Rb2SnCu3F12 shows particularly unusual behaviour; for powder samples at temperatures below ambient, a structurally re-entrant phase transition is observed, with the intermediate phase being a complex triclinic unit cell. This is not the case for single crystals, however, making the exact nature of the intermediate phase challenging to ascertain [13]. The largest reported B′ cation is Ce4+ [15]. At room temperature, there is a major “corrugation” distortion of the kagome layer, caused by the coordination requirements of the larger Ce4+, which in this case is eight-coordinated. This inherent distortion leads to a complex ferromagnetically-ordered structure that is far removed from the highly frustrated ground state of interest. As this brief review of the A2B′Cu3F12 family shows, there is a large degree of substitutional flexibility in this structure type that leads to a number of significantly different structural (and magnetic) behaviours. Further variation of the constituent ions may lead to a material that retains its ideal kagome lattice down to the lowest temperatures, thus improving the chances of finding exotic magnetic ground states related to extreme frustration. When B′ increases in size (for Cs2 B′Cu3F12, B′ = Zr4+, Hf4+ and Ce4+), it is clear that the perfect kagome lattice is lost, due to the coordination demands of such large cations. When B′ is relatively large, but cannot support greater than six-coordinate environments (Cs2SnCu3F12), there appear to be other more subtle factors that encourage symmetry-breaking of the kagome lattice.
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On the contrary, if A is too small (Rb2SnCu3F12) there is also the presence of a distortion. This complex interplay of cation size matching, which apparently dictates structural distortion away from the ideal kagome geometry, with subsequent loss of magnetic frustration, has motivated us to expand the range of known members of this family. By decreasing the size of the B′ cation further, i.e., by incorporation of Ti4+, we have now produced the two novel materials Cs2TiCu3F12 and Rb2TiCu3F12. These represent the extremes of A/B′ cation size ratio and minimum A and B′ absolute cation size, respectively. 2. Results and Discussion 2.1. Single Crystal X-ray Diffraction of Cs2TiCu3F12 Cs2TiCu3F12 was obtained in the form of single crystals, and these were subject to SCXD analysis (further details are provided in ESI, Table S1). As expected, the lattice parameters are smaller than those found for other members of the Cs2 B′Cu3F12 family and there is a particular reduction in the c-axis direction (Table 1). Table 1. Lattice parameters (and Shannon radii) for the title compound and the three other reported members of the Cs2 B′Cu3F12 family, in space group R3̅m at room temperature. M4+ Ti4+ Sn4+ (11) Hf4+ (11) Zr4+ (11)
Ionic Radius [16] 0.605 0.69 0.71 0.72
a (Å) 7.1014(14) 7.142(4) 7.163 7.166
c (Å) 19.955(2) 20.381(14) 20.49 20.46
At room temperature, the structure is found to be similar to that described for single crystals of Cs2SnCu3F12 (Table S2 in ESI). A comparison of bonding geometries (Table 2) reveals that the accommodation of the significantly smaller TiF6 octahedron causes only small changes in CuF6 geometry, but does lead to a significant shift of the Cs+ cation of approximately 0.1 Å along the c-axis, i.e., the Cs+ ion moves out of the hexagonal kagome “pore” and towards the smaller TiF6 octahedron (Figure 2). The Cs–Cs distance for the Ti4+ case is 4.4220(12) Å and for Sn4+ it is 4.317(3) Å. Table 2. Metal—fluorine bonds and Cu–Cu distances (Å) for Cs2TiCu3F12 and Cs2SnCu3F12 (R3̅m model at room temperature). Bond Cs–F1 (×3) Cs–F2 (×3) Cu–F1 (×4) Cu–F2 (×2) M4+–F2 (×6) Cu–Cu (×4)
Cs2TiCu3F12 3.101(4) 3.352(4) 1.9037(14) 2.333(4) 1.864(4) 3.551
Cs2SnCu3F12 [11] 3.124(2) 3.411(2) 1.8969(11) 2.346(2) 1.9527(15) 3.571
On cooling to 125 K, it is found that a phase transition has occurred. The unit cell is found to have doubled in the ab-plane and the symmetry reduced to R3̅ (comparative refinements in the higher symmetry R3̅m gave significantly poorer fits), which is similar to that reported previously in reduced
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temperature single crystal studies of Cs2SnCu3F12 [11]. It was indeed anticipated that there would be a greater similarity between the Ti4+ system and the Sn4+ system, rather than the Zr4+ analogue, as the phase transition in the latter is driven by a requirement for Zr4+ to attain seven-coordination. This was not expected for either of the smaller B′ cations. This observed low-temperature superlattice is similar to that reported for Rb2SnCu3F12 at room temperature; however, in the present case there is no disorder of the fluorine atoms, as is found for Rb2SnCu3F12 (ESI, Figure S1).
Figure 2. Hexagonal pore through the kagome lattice; the dashed line links the two opposing Cs+ ions. We suggested that for Cs2SnCu3F12 the low temperature phase transition was motivated by Sn4+ being over-bonded; through the phase transition the Sn–F bond length increased thus partially relieving this over-bonding. For Cs2TiCu3F12 this is also found to be partially the case—some Ti–F bond lengths are longer for the 125 K structure. For the coordination sphere of Ti1, there has been a small decrease in bond length but for the more prevalent Ti2 (3 × per unit cell) there has been an increase (Table 3). This leads to an overall slight decrease in BVS (also, Table 3). Table 3. Ti–F bond distances for Cs2TiCu3F12 as found from SCXD at room temperature (R3̅ m) and 125 K (R3̅ ) and BVS for Ti4+ atoms at both room temperature and 125 K, calculated using VaList [17]. Bond
RT Distance (Å)
Ti1–F2 (×6)
1.864(4)
Atom
BVS
Ti1
4.53
Average
4.53
125 K Bond Distance (Å) Ti1–F5 (×6) 1.863(9) Ti2–F7 (×2) 1.871(9) Ti2–F6 (×2) 1.871(7) Ti2–F8 (×2) 1.872(8) Atom BVS Ti1 4.72 Ti2 4.33 Average 4.43
Qualitatively, there is a skewing of the kagome lattice which gives rise to two different Cu sites (1:1 ratio) and two different Cu3 triangles (3:1 ratio), one of which remains strictly equilateral (Cu···Cu = 3.551 Å; equal to that at room temperature), and the other with to three distinct Cu···Cu distances (range 3.51–3.57 Å). The degree of distortion is therefore not as great as that seen in Rb2SnCu3F12. This is correlated with the rotations of the TiF6 octahedra around the c-axis; 3/4 are rotated
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one way and 1/4 are rotated in the opposite sense (Figure 3). This octahedral rotation lowers the symmetry from R3̅ to R3̅m.
Figure 3. Structure of Cs2TiCu3F12 in the low-temperature 𝑅3̅ phase. Note the rotations of the TiF6 octahedra (foreground) against Cu–F kagome background; a quarter of TiF6 octahedra are rotated in a contrary sense. 2.2. Powder Diffraction Study of Cs2TiCu3F12 In order to reveal further details about the nature of the phase transition found for the single crystal, a powder X-ray diffraction (PXRD) study was carried out. At room temperature, the single crystal model of Cs2TiCu3F12, as reported above was confirmed, with lattice parameters, from PXRD, a = 7.090321(18) Å and c = 19.91021(9) Å. This model also provides an excellent fit to the neutron powder diffraction (NPD) data. Details of these refinements, and examples of Rietveld fits, are presented in Table S3 and Figure S2. There is very little difference in the structures determined by the three diffractometry methods used. Synchrotron X-ray powder diffraction (SXPD), however, shows some interesting artefacts relating to the sample morphology. Anisotropic peak broadening is apparent (Figure 4) and has been taken into account using a technique developed by Stephens [18] and implemented using the GSAS program. The broadening is particularly accentuated on the (003), (006) and (009) peaks which is indicative of a platy morphology Use of the Scherrer formula allows the calculation of an approximate particle size; from the (003) peak it is found the particle size is ~1200 Å and from the (110) peak the particle size is found to be ~2000 Å. On reducing the sample temperature to 100 K, there is a clear splitting of some peaks in the SXPD patterns, indicating that there has been a lowering of symmetry. Indexing, using the DICVOL91 program, [19] suggests a monoclinic unit cell with the metrics a ≈ 10.44 Å, b ≈ 7.04 Å, c ≈ 7.76 Å, β ≈ 96.9°. There are a number of possible distortions of the parent rhombohedral cell that lead to a monoclinic cell of these metrics. Use of the ISODISTORT program [20] leads to five key possibilities (space groups I2/m, P2/m, P21/m, P2/n, P21/n) although this is quickly narrowed down to P21/n or P2/n due to the presence of reflections indexable as h + k + l = 2n (eliminating body-centred cells) and all h0l
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satisfying h + l = 2n (n-glide plane). From these, P21/n is selected due to superior statistics in Rietveld refinement (Table S4). Assessment of the model produced by Rietveld refinement of the low temperature data (Table S5) suggests that it is isostructural to that found for Cs2SnCu3F12 at low temperature. Bond distances are reported in Table 4. In this model, there are also two distinct Cu sites (this time in a 2:1 ratio), but only one type of Cu3 triangle, leading to three different Cu···Cu distances (range 3.51–3.57 Å).
Figure 4. A selection of SXPD reflections for Cs2TiCu3F12 at 300 K. Note the broadening of the (0,0,9) reflection compared to (2,1,4), indicative of an anisotropy in crystallite shape. Table 4. Selected metal-fluoride distances for Cs2TiCu3F12 at 100 K as derived from SXPD data (P21/n model). Metal—Fluoride Bond Cs–F3 Cs–F1 Cs–F2 Cs–F4 Cs–F5 Cs–F5 Cs–F6 Cu1–F2 (×2) Cu1–F1 (×2) Cu1–F6 (×2) Cu2–F3 Cu2–F1 Cu2–F2 Cu2–F3 Cu2–F4 Cu2–F5 Ti–F6 (×2) Ti–F4 (×2) Ti–F5 (×2)
Bond Length (Å) 3.051(4) 3.086(5) 3.102(5) 3.185(5) 3.201(5) 3.242(5) 3.275(5) 1.912(6) 1.917(6) 2.310(6) 1.875(5) 1.903(6) 1.921(6) 1.952(5) 2.319(6) 2.325(6) 1.835(4) 1.843(5) 1.896(5)
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On analysis of the full temperature range (Table S6), it is found that the phase transition occurs between 240 and 260 K and can be tracked by comparing SXPD patterns at different temperatures (Figure 5) and also by observing the change of unit cell volume as a function of temperature (Figure 6). The transition is characterised by a direct reduction in symmetry at 240 K from rhombohedral to monoclinic, with no evidence of a mixed phase region. This transition is analogous to that observed in powder samples of Cs2SnCu3F12 but occurs at a higher temperature (240 K versus 170 K) [12] possibly as a result of the smaller B-site cation. This transition leads to a “tilting” of the TiF6 octahedra out of the ab plane, into layers in an A-B-A-B pattern (Figure 7). A closer analysis of the structural details gives a possible motivation for this—as in the single crystal case (above), the powder shows an over-bonded Ti4+ at room temperature and down to 260 K. On crossing the transition—and losing symmetry—the Ti4+ shows a sudden drop in BVS, while the Cs+ shows a sudden increase (Table 5).
Figure 5. SXPD patterns for Cs2TiCu3F12 at a range of temperatures; note peak splittings appearing below 260 K.
Figure 6. Unit cell volume per formula unit vs. temperature for Cs2TiCu3F12 powder as derived from SXPD data. Note the change in gradient indicated by the shaded area.
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Figure 7. Tilting of TiF6 octahedra (foreground) in an A-B-A-B fashion against a Cu–F kagome background as found in Cs2TiCu3F12 below the rhombohedral → monoclinic transition temperature. Table 5. Bond valence sums for the cations in Cs2TiCu3F12 as a function of temperature (VaList. [17]). Bond lengths derived from SXPD data. Temperature (K) 300 280 260 240 220 200 100
4+
Ti 4.884 4.884 4.884 4.934 4.714 4.676 4.616
BVS Cu1 Cu22+ 2.016 2.012 2.014 1.990 2.037 1.950 2.009 1.954 2.002 1.970 1.975 2+
Cs+ 0.858 0.867 0.870 0.919 0.946 0.961 1.019
The suggestion in this case is that, again, the transition is motivated by the need for both Ti4+ and Cs+ to attain a more optimal bonding environment, and the high temperature phase is stabilized by entropy effects. 2.3. Comparison of Single Crystal and Powder Samples of Cs2TiCu3F12 It is clear from the above that single crystal and powder samples of Cs2TiCu3F12 show differing behaviours with respect to their lower temperature phase transitions, suggesting some form of crystallite size dependence to the phase transition behaviour. For the powder at low temperatures, the doubled rhombohedral cell found for the single crystal is not compatible with the SXPD data: i.e., key splittings are not accounted for (Figure S3). A similar analysis can be performed for the single crystal data: using a selection of images it can be seen that the smaller, primitive monoclinic unit cell is not adequate to fit
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all the reflections, whereas the doubled rhombohedral model is found to fit well (Figure S4). The differing natures of the distortions of the underlying Cu–Cu kagome frameworks for the two polymorphs are illustrated graphically in Figure S5. The reasons for this particular morphology dependent polymorphism are unknown, although the general theme has come under scrutiny in the past. There have been a number of studies that have correlated surface energy to phase transition temperature/pressure and polymorphism [21–23]. These have focused on comparing bulk and nano-particulate systems and suggest that surface energy is a dominant factor and this may be the case for Cs2TiCu3F12. Another consideration is the platy nature of the powdered crystallites—this may allow extra degrees of freedom and the adoption of a lower energy polymorph that is not available to the single crystal. Differing degrees of minor disorder (e.g., on the fluoride sublattice), which are not detectable at the limit of powder diffraction, might also be involved. Purely kinetic effects can also not be ruled out. A computational study of the energetics of these different polymorphs would be of interest. 2.4. Powder X-ray Diffraction of Rb2TiCu3F12 Synthesis of diffraction quality single crystals of Rb2TiCu3F12 proved challenging and so our results for this novel material will be based on SXPD and NPD data (Figure S6). At room temperature, Rb2TiCu3F12 is found to adopt a triclinic unit cell, space group P1̅. This is related to the doubled rhombohedral cell (as reported for Rb2SnCu3F12 at room temperature [14]) by the transformation matrix (2/3, 1/3, 1/3),(−1/3, 1/3, 1/3),(−1/3, −2/3, 1/3) where a = b = c and α = β = γ, for the ideal case. This primitive triclinic unit cell is similar to that reported for the intermediate phase of Rb2SnCu3F12 [13]. Lattice parameters are as shown in Table 6, showing slight discrepancies between the two techniques. The lattice parameters determined for the impurity phases, from the same datasets, also differ slightly (Tables S7 and S8); the inclusion of the impurities in the Rietveld refinements impedes the extraction of accurate values for the parameters of all phases, and this is the likely to be the main cause of the discrepancies, although we cannot rule out our temperature variations or other minor systematic errors. Table 6. Comparison of room temperature lattice parameters of Rb2TiCu3F12 from SXPD and NPD data. Unit Cell Parameter a (Å) b (Å) c (Å) α (°) β (°) γ (°)
SXPD 10.3592(8) 10.3506(9) 10.3440(3) 83.838(8) 83.832(8) 83.9111(15)
NPD 10.3703(15) 10.3521(19) 10.3369(14) 83.717(17) 83.635(14) 83.921(8)
Due to the complex triclinic model used (38 unique atoms, Table S9) it is not possible to refine the atomic coordinates reliably and so detailed comment on the atomic structure is not appropriate. Despite this, there are still some conclusions that may be drawn from the variation in unit cell metrics versus temperature. On cooling it can be seen that the unit cell further diverges from the pseudo-rhombohedral
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ideal case (i.e., where a = b = c and α = β = γ) indicating that the sample is becoming more distorted from the parent rhombohedral phase (Tables S10 and S11). Hence, we propose that Rb2TiCu3F12 will transform to the rhombohedral form at a temperature above the highest measured; by extrapolation it is suggested that this transition may occur between 320 and 350 K (Figure 8).
Figure 8. Lattice parameters derived from SXPD data for Rb2TiCu3F12 powder as a function of temperature (error bars included). Another feature notable in the data is a hysteresis between ~150 and 300 K; the lattice parameters on heating and cooling cycles are not superimposable, as they are at lower temperatures. This indicates that the phase transition may be first order. It should be noted that there is no observable hysteresis in the unit cell volume parameter, however. 2.5. Magnetic Properties of Cs2TiCu3F12 0.01774 g of Cs2TiCu3F12 powder of approximately 80% purity (0.0581 mM Cu2+) was synthesised especially for magnetic measurements (see Experimental Section). The sample was cooled to 2 K and a field of 2 kOe applied before heating to 190 K while measuring the magnetisation (zero field cooled,
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ZFC). The sample was then re-cooled in the 2 kOe external field to 2 K before heating to 300 K and measuring the magnetisation (field cooled, FC). Both ZFC and FC data (Figure 9) show a large anomaly beginning at ~21 K and peaking at ~16 K. There is some discrepancy between the ZFC and FC data, probably due to the presence of a magnetically-ordered impurity phase. Linear behaviour was observed for 1/χm versus T between 150 and 300 K and a Curie-Weiss fit yielded an effective moment of 1.77 to 1.84 μB, as expected for Cu2+ in octahedral environments (see, for example, [24]). The Curie-Weiss temperature was found to be −264 to −350 K, indicating strong antiferromagnetic interactions.
Figure 9. The zero-field cooled (ZFC) and field-cooled (FC) magnetic susceptibility data for a powder sample of Cs2TiCu3F12. The inset shows the inverse susceptibility with Curie-Weiss fits (red) to the linear sections of the data. The variation of structural properties with particle size in these samples, as discussed above, is also reflected in the magnetic properties. ZFC and FC magnetic susceptibility data were measured in a magnetic field of 2 kOe, on a collection of unground single crystals (0.003 g, 0.0123 mM Cu2+). These data are clearly different from those of the powder sample; there is a divergence between the ZFC and FC susceptibility below 340 K, but also what at first sight appears to be a large temperature independent paramagnetic contribution (TIP) (Figure 10). These data show two low temperature anomalies; one at 16 K and one at 4.8 K. The higher temperature anomaly is slightly lower in temperature, and much smaller in magnitude, than that found for the powder. Attempts to model the data with a combination of TIP and a single Curie-Weiss contribution, i.e., with the equation: χm = χ0 + 𝐶⁄(𝑇 + 𝑇 ) cw
(1)
do not lead to satisfactory fits. It therefore is likely that even in these samples composed of a small number of discrete crystallites, more than one magnetic phase is present and it is not possible to identify their individual contributions.
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Figure 10. The zero-field cooled (ZFC) and field-cooled (FC) magnetic susceptibility data for a single crystal sample of Cs2TiCu3F12 (red) compared to the powder-sample susceptibility (black), both measured in an applied magnetic field of 2 kOe. 3. Experimental Section Syntheses were performed in a number of ways depending on whether powder or single crystalline samples were required. For powder crystallographic studies, solid-state synthesis via reaction under flowing argon was performed. As TiF4 is volatile below the reaction temperature, the precursor A2TiF6 (A = Cs, Rb) was first synthesised, by a route similar to that described in [25]. CsCl (2 mM, Sigma Aldrich, 99%, Dorset, UK) or RbCl (2 mM, Sigma Aldrich, 99.8%) and TiO2 (1 mM, ~99%) were mixed with deionised water (4 mL) in a 40 mL Teflon lined autoclave. Ethylene glycol (5 mL, Fisher Scientific, >99%) and HF(aq) (1 mL, 48%–51%, Alfa Aesar, Heysham, UK) were then added to the autoclave, which was then sealed and heated under autogenous pressure at 433 K overnight. The resulting crystalline powders were then isolated by filtration, washing with water:ethylene glycol (1:1) and then dried overnight at ~330 K in air. The resulting A2TiF6 powders were then dried at 390 K and ~10−4 mbar for 24 h. The A2TiF6 powders were then mixed with CuF2 (Sigma Aldrich, 98%) in stoichiometric amounts (1:3) in an argon filled glove box. This mixture was ground and sealed in a gold tube by crimping the ends. The gold tube was then heated under flowing argon in the following manner: 20 K·min−1 373–873 K, 12 h at 873 K, 20 K·min−1 873–373 K. The resulting grey coloured powder was typically found to be 94% pure in the case of Cs2TiCu3F12 and 88% pure for Rb2TiCu3F12. Notable impurities (all
